Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often ...takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, and robust principal component analysis. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.
SARS-CoV-2 causes the recent global COVID-19 public health emergency. ACE2 is the receptor for both SARS-CoV-2 and SARS-CoV. To predict the potential host range of SARS-CoV-2, we analyzed the key ...residues of ACE2 for recognizing S protein. We found that most of the selected mammals including pets (dog and cat), pangolin and Circetidae mammals remained the most of key residues for association with S protein from SARS-CoV and SARS-CoV-2. The interaction interface between cat/dog/pangolin/Chinese hamster ACE2 and SARS-CoV/SARS-CoV-2 S protein was simulated through homology modeling. We identified that N82 in ACE2 showed a closer contact with SARS-CoV-2 S protein than M82 in human ACE2. Our finding will provide important insights into the host range of SARS-CoV-2 and a new strategy to design an optimized ACE2 for SARS-CoV-2 infection.
•Pets (dog and cat), pangolin and Circetidae remained the key residues for association with S from SARS-CoV and SARS-CoV-2.•The interface of the interaction between cat/dog/pangolin/Chinese hamster ACE2 and SARS-CoV/SARS-CoV-2 RBD was simulated.•N82 of ACE2 showed a closer contact with SARS-CoV-2 S than M82, suggesting an optimized ACE2 for SARS-CoV-2 infection.
We present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. This paper leverages ...recent results that provide an exact characterization of the performance of the spectral method in the high-dimensional limit. This characterization allows us to map the task of optimal design to a constrained optimization problem in a weighted <inline-formula><tex-math notation="LaTeX">L^2</tex-math></inline-formula> function space. The latter has a closed-form solution. Interestingly, under a mild technical condition, our results show that there exists a fixed design that is uniformly optimal over all sampling ratios. Numerical simulations demonstrate the performance improvement brought by the proposed optimal design over existing constructions in the literature. In a recent work, Mondelli and Montanari have shown the existence of a weak recovery threshold below which the spectral method cannot provide useful estimates. Our results serve to complement that work by deriving the fundamental limit of the spectral method beyond the aforementioned threshold.
For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of ...memory and computational resources in a timely manner for decision making. This often is coupled with the missing data problem, such that only a small fraction of data attributes are observed. These complications impose significant, and unconventional, constraints on the problem of streaming principal component analysis (PCA) and subspace tracking, which is an essential building block for many inference tasks in signal processing and machine learning. This survey article reviews a variety of classical and recent algorithms for solving this problem with low computational and memory complexities, particularly those applicable in the big data regime with missing data. We illustrate that streaming PCA and subspace tracking algorithms can be understood through algebraic and geometric perspectives, and they need to be adjusted carefully to handle missing data. Both asymptotic and nonasymptotic convergence guarantees are reviewed. Finally, we benchmark the performance of several competitive algorithms in the presence of missing data for both well-conditioned and ill-conditioned systems.
In vector space model (VSM), text representation is the task of transforming the content of a textual document into a vector in the term space so that the document could be recognized and classified ...by a computer or a classifier. Different terms (i.e. words, phrases, or any other indexing units used to identify the contents of a text) have different importance in a text. The term weighting methods assign appropriate weights to the terms to improve the performance of text categorization. In this study, we investigate several widely-used unsupervised (traditional) and supervised term weighting methods on benchmark data collections in combination with SVM and kNN algorithms. In consideration of the distribution of relevant documents in the collection, we propose a new simple supervised term weighting method, i.e. tf.rf, to improve the terms' discriminating power for text categorization task. From the controlled experimental results, these supervised term weighting methods have mixed performance. Specifically, our proposed supervised term weighting method, tf.rf, has a consistently better performance than other term weighting methods while other supervised term weighting methods based on information theory or statistical metric perform the worst in all experiments. On the other hand, the popularly used tf.idf method has not shown a uniformly good performance in terms of different data sets.
To date, liquid metals have been widely applied in many fields such as electronics, mechanical engineering and energy. In the last decade, with a better understanding of the physicochemical ...properties such as low viscosity, good fluidity, high thermal/electrical conductivity and good biocompatibility, gallium and gallium-based low-melting-point (near or below physiological temperature) alloys have attracted considerable attention in bio-related applications. This tutorial review introduces the common performances of liquid metals, highlights their featured properties, as well as summarizes various state-of-the-art bio-applications involving carriers for drug delivery, molecular imaging, cancer therapy and biomedical devices. Challenges for the clinical translation of liquid metals are also discussed.
Severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) causes the recent COVID‐19 public health crisis. Bat is the widely believed original host of SARS‐CoV‐2. However, its intermediate host ...before transmitting to humans is not clear. Some studies proposed pangolin, snake, or turtle as the intermediate hosts. Angiotensin‐converting enzyme 2 (ACE2) is the receptor for SARS‐CoV‐2, which determines the potential host range for SARS‐CoV‐2. On the basis of structural information of the complex of human ACE2 and SARS‐CoV‐2 receptor‐binding domain (RBD), we analyzed the affinity to S protein of the 20 key residues in ACE2 from mammal, bird, turtle, and snake. Several ACE2 proteins from Primates, Bovidae, Cricetidae, and Cetacea maintained the majority of key residues in ACE2 for associating with SARS‐CoV‐2 RBD. The simulated structures indicated that ACE2 proteins from Bovidae and Cricetidae were able to associate with SARS‐CoV‐2 RBD. We found that nearly half of the key residues in turtle, snake, and bird were changed. The simulated structures showed several key contacts with SARS‐CoV‐2 RBD in turtle and snake ACE2 were abolished. This study demonstrated that neither snake nor turtle was the intermediate hosts for SARS‐CoV‐2, which further reinforced the concept that the reptiles are resistant against infection of coronavirus. This study suggested that Bovidae and Cricetidae should be included in the screening of intermediate hosts for SARS‐CoV‐2.
Research Highlights
Affinities to SARS‐CoV‐2 S protein of the 20 key residues in ACE2 from mammal, bird, turtle and snake were analyzed.
ACE2 proteins from Primates, Bovidae, Cricetidae and Cetacea were predicted to associate with SARS‐CoV‐2 RBD.
Neither snake nor turtle was the intermediate hosts for SARS‐CoV‐2
The rapid advancement of the internationalization process has led to the gradual labeling and commoditization of commercial space, which is detached from the connotation of regional culture. This ...paper establishes a commercial space layout model and a commercial space layout optimization design process based on Bayesian network, combined with the geometric characteristics and layout attributes of commercial space layout. It also utilizes Simpson’s index and kernel density analysis to explore the influencing factors of regional culture integration into commercial space design and finally takes the design of comprehensive commercial space with regional characteristics of culture in the Central Plains as a research case to specifically explore the feasibility of integrating regional cultural characteristics into commercial space design. The results show that in the process of designing the commercial space of regional culture in the Central Plains, the audiovisual comfort reaches its best when the space aspect ratio is about 1.42 and the color saturation is about 25.05. The layout effect is the best with a visual exposure degree of 995 for the row and column layout. The integration of regional culture into commercial space design can be referenced by this study.
A facile approach for preparation of photoluminescent (PL) carbon dots (CDs) is reported. The three resulting CDs emit bright and stable red, green and blue (RGB) colors of luminescence, under a ...single ultraviolet‐light excitation. Alterations of PL emission of these CDs are tentatively proposed to result from the difference in their particle size and nitrogen content. Interestingly, up‐conversion (UC)PL of these CDs is also observed. Moreover, flexible full‐color emissive PVA films can be achieved through mixing two or three CDs in the appropriate ratios. These CDs also show low cytotoxicity and excellent cellular imaging capability. The facile preparation and unique optical features make these CDs potentially useful in numerous applications such as light‐emitting diodes, full‐color displays, and multiplexed (UC)PL bioimaging.
On the dot: A facile approach to photoluminescent carbon dots (CDs) that can be excited by a single wavelength and demonstrate emission of the three primary colors (red, green, and blue) is reported. The resulting CDs can be potentially used in the fabrication of flexible full‐color emission films and in multicolor cellular imaging.
A novel hybrid material with excellent microwave absorption property has been designed by decorating reduced graphene oxide with Ba Tb
0.2
Eu
0.2
Fe
11.6
O
19
/PANI composite, and the effect of ...graphene content on microwave absorption property has been investigated. The microstructure of the composite is characterized by X-ray diffraction, Fourier-transform infrared spectroscopy, field emission scanning electron microscope, transmission electron microscope and Raman spectroscopy. The mechanism of microwave absorption is discussed minutely. The result shows that the ternary nanocomposites demonstrate unexceptionable microwave absorption property due to its special nanostructures and synergistic effect among BaTb
0.2
Eu
0.2
Fe
11.6
O
19
, PANI and RGO. The minimum reflection loss can reach − 60.9 dB at 16.4 GHz with a thickness of only 1.95 mm, and the corresponding effective absorption bandwidth (below − 10 dB) is 4.2 GHz. BaTb
0.2
Eu
0.2
Fe
11.6
O
19
/PANI/RGO composite can be one of the most promising microwave absorption materials.
PDF
